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Mathematics Colloquium
Contact: Federico Ardila
Time and Location: Wednesdays, 4:10-5:00 pm in Thornton Hall 211.
Refreshments: 3:30 pm in Thornton Hall 935.
Past colloquia: videos and
abstracts.
Dates for Spring 2008:
Feb 6 Feb 20 March 6,7 Mar 19 Apr 9 May 7
February 6, 2008
Sergey Fomin
University of Michigan
| TITLE:
Cluster Algebras.
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ABSTRACT:
Cluster algebras arise in various algebraic and geometric contexts,
with combinatorics providing a unifying framework. My presentation
of the basic definitions and results of this emerging theory will
be guided by two sets of examples: coordinate rings of classical
algebraic varieties, and cluster algebras associated with bordered
oriented surfaces with marked points.
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4:10 PM in TH 211 |
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refreshments
served in TH 935 at 3:30 PM |
February 20, 2008
Francisco Santos
Universidad de Cantabria, Santander, Spain
| TITLE: Graphs of triangulations.
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ABSTRACT: I will give an introduction to the "graph of flips" between
triangulations of a polytope (its definition, its connections to
algebraic geometry, geometric combinatorics, and combinatorial
topology) and review the disconnected graphs of flips that I have
constructed in recent years, in dimensions five and six.
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4:10 PM in TH 211 |
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refreshments
served in TH 935 at 3:30 PM |
March 6, 2008
Pamela Fong Symposium
Richard Stanley
Massachusetts Institute of Technology
| TITLE: A survey of plane tilings.
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ABSTRACT: We will survey some of the highlights of the theory of plane
tilings, focusing on tiling a bounded region of the plane with
finitely many tiles. A standard example, though not very
mathematical, is a jigsaw puzzle. We consider such questions as the
following: (1) Is there a tiling? (2) How many tilings are there? (3)
About how many tilings are there? (4) Is a tiling easy to find? (5) Is
it easy to prove or to convince someone that a tiling doesn't exist?
(6) What does a typical tiling look like? We point out some
interesting connections between tilings and such topics as computer
science, continued fractions, probability theory, and mathematical
logic.
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4:10 PM in HSS 317
March 7, 2008
Pamela Fong Symposium
Richard Stanley
Massachusetts Institute of Technology
| TITLE: Increasing and decreasing subsequences.
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ABSTRACT: A subsequence of a permutation of 1,2,..., n is *increasing* if its elements appear in increasing order. For instance, 4578 is an
increasing subsequence of 43571826. A *decreasing subsequence* is
similarly defined. We will survey the subject of increasing and
decreasing subsequences, focusing on what can be said about the
longest increasing and longest decreasing subsequence of a
permutation. Topics will include (a) relationship to Young tableaux
and the famous RSK algorithm, (b) the asymptotic behavior of the
length of the longest increasing subsequence (due to Baik, Deift, and
Johansson), (c) connections with random matrix theory, and (d) an
extension of the theory from permutations to complete matchings.
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4:10 PM in SCI 210
March 19, 2008
Mariana Ferreira
Department of Anthropology
San Francisco State University
| TITLE: The Mathematics of Gift-Exchange in the Brazilian Amazon. |
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ABSTRACT:
This presentation discusses how values and symbolic properties of both gift exchange and capitalist economics structure arithmetic dilemmas in the Brazilian Amazon. By articulating principles of the gift with those of capitalist economic action, Indigenous Peoples highlight the ways in which mathematical knowledge is constituted in everyday practice, challenging functional assumptions about cognition and schooling. Gift-exchange also informs Indigenous environmental theories about the collective allocation of land and natural resources. Successful Indigenous GIS-GPS map-making initiatives in Central-Brazil rely on community-based participatory research methodology to advocate for human rights and propose new insights into how mathematical knowledge is built throughout history in different socio-cultural environments.
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4:10 PM in TH 211 |
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refreshments
served in TH 935 at 3:30 PM |
April 9, 2008
Steven Krantz
Washington University
| TITLE:
Analysis on the Worm Domain.
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ABSTRACT:
In joint work with Marco Peloso, we study the Bergman
kernel on the classical worm domain of Diederich
and Fornaess. A detailed asymptotic expansion for
the worm is obtained. This yields important results
about mapping properties of the Bergman projection, and
also important irregularities of the Bergman kernel and projection.
Prerequisites for this talk are minimal. A graduate student
with a course in complex variables should be able to
understand the key ideas.
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4:10 PM in TH 211 |
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refreshments
served in TH 935 at 3:30 PM |
May 7, 2008
Gitta Kutyniok
Stanford University
| TITLE: Geometric Separation via l_1 Minimization and Sparsity.
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ABSTRACT: Modern data is often composed of two (or more) morphologically distinct
constituents - for instance, pointlike and curvelike structures in astronomical
imaging of galaxies. Although it seems impossible to extract those components
- as there are two unknowns for every datum - suggestive empirical results have
already been obtained. In this talk we first give a general introduction into
geometric separation problems and discuss the recent avalanche of work which
uses the methodology of l_1 minimization and sparsity. We then present the
first theoretical approach to the geometric separation of pointlike and curvelike
structures based on the overcomplete systems of radial wavelets and curvelets or
of orthonormal wavelets and shearlets which sparsify the different components.
As our main result we prove that using a particular form of l_1 minimization
as the decomposition technique achieves in fact arbitrarily perfect separation
of pointlike and curvelike structures. This is joint work with David Donoho
(Stanford University).
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